Abstract
An explicit numerical method to solve a fractional cable equation which involves two temporal Riemann‐Liouville derivatives is studied. The numerical difference scheme is obtained by approximating the first‐order derivative by a forward difference formula, the Riemann‐Liouville derivatives by the Grünwald‐Letnikov formula, and the spatial derivative by a three‐point centered formula. The accuracy, stability, and convergence of the method are considered. The stability analysis is carried out by means of a kind of von Neumann method adapted to fractional equations. The convergence analysis is accomplished with a similar procedure. The von‐Neumann stability analysis predicted very accurately the conditions under which the present explicit method is stable. This was thoroughly checked by means of extensive numerical integrations.
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